In a CDAR problem [1]}, a labeled source domain \(\mathcal {D}_s = \lbrace (\mathbf {x}_i, y_i)\rbrace _{i=1}^{n_s}\)  and an unlabeled target domain \(\mathcal {D}_t = \lbrace \mathbf {x}_j \rbrace _{j=1}^{n_t}\)  are given, where \(n_s\)  and \(n_t\)  are the number of source and target samples respectively. In our problem, \(\mathcal {D}_s\)  and \(\mathcal {D}_t\)  have the same feature spaces and label spaces, i.e. \(\mathcal {X}_s = \mathcal {X}_t \subset \mathbb {R}^d\)  and \(\mathcal {Y}_s = \mathcal {Y}_t\) , where \(d\)  is the feature dimension. \(y_s, y_t \in \lbrace 1, \cdots , C \rbrace \) , and \(C\)  is the number of classes. Two domains have different distributions, i.e., \(p_s(\mathbf {x},y) \ne p_t(\mathbf {x}, y)\) . The goal of cross-domain learning is to obtain the labels \(y_t\)  for the target domain with the help of the source domain \(\mathcal {D}_s\) .
